Question

prove that if A and B are antisymetric matrix than these are antisymetric too A^T ,A+B,A-B and k*A .please

Answer 1

antisymetric means:\[A=-A^T,B=-B^T\]
So looking at A^T we obtain:\[A^T=-A=-(A^T)^T\]so because:\[A^T=-(A^T)^T\]it is anti symmetric.

Answer 2

\[A+B=-A^T-B^T=-(A^T+B^T)=-(A+B)^T\]

Answer 3

The last two will follow the same idea.

Answer 4

thank you ..i should do the same thing with this too ?:if C is a whatever matrix and C^T *B*C exists and B is antisymetric then C^T *B*C is antisimetryc too

Answer 5

yeah it will work out the same

Answer 6

what should I do to prove that if A is a symetric matrix than
2*A^2-3*A+I (unit matrix) is symetric too